As soundtracks have become de rigueur in blockbuster exhibitions – jungle noises and bellowing elephants to bring history alive – I wonder when conceptual art shows will start getting a laughter track. A lot of works in this retrospective of one of the most influential artists of our time could easily be accompanied by recorded titters – just to break the mood of Tate severity and remind people they can laugh.

Here is Baldessari's 1972-73 set of photographs called The Artist Hitting Various Objects With a Golf Club. It's as entertaining as the title suggests. Here, too, is a set of photos of him trying to blow cigar smoke to imitate a picture of a cloud, and another series in which he stands waving to boats as they go by. Wistful, witty, these early works have given so many ideas to younger artists that his exhibition is in danger of ruining other peoples' reputations. It's not just the jokers among current artists who owe him, either; his cinematic works that arrange photographs in narratives linked by sketched arrows and scrawled notes anticipate Tacita Dean.

After burning all his conventional works, he set out to dispense with a coherent style or look, and to make art in which the idea alone matters. On his paintings appear texts written by a signwriter – including a quotation from critic Clement Greenberg saying art is about aesthetic impact, not ideas. Baldessari, of course, believed the exact opposite.

In the 1970s, Baldessari cracked one great joke after another. Then as Reagan came to power, he turned to making large-scale photomontages that often labour simplistic points. This seems irrelevant compared with his revolutionary elaboration of the fun nature of conceptual art. I'm still laughing at his 1973 piece in which a couple read a cinema manual and realise what's wrong with their independent films: they didn't know you could actually move the camera.